Application of Weighted Fuzzy Clustering Method to Supplier Selection under
E-business
Yan Yang1,a, Wei-ping Yang2,b, Yao Liang3,c
1
2
Department of Industrial Engineering, Kunming University of Science and Technology, Kunming, China
Department of Industrial Engineering, Kunming University of Science and Technology, Kunming, China
3
Adult Education College, Kunming University of Science and Technology, Kunming, China
(axyxy_1340@163.com, bywp58@yahoo.com.cn)
Abstract: In order to avoid the imbalance among
evaluation index in the general fuzzy clustering, using the
weighted fuzzy clustering algorithm to choose the best
provider under E-business. In this paper, first，the weighted
of each index is curtained by AHP, and then the weight is
added to the fuzzy clustering algorithm. The F-distribution
of probability statistics is used to determine the best
classification number, which can help choose the best
classification. Finally, comprehensive value is computer by
fuzzy synthetically evaluation, through which the best
supplier can be selected.
Keywords: Analytic hierarchy process; Fuzzy
synthetically evaluation; Weight fuzzy clustering; Provider
selection
I Introduction
The twenty-first Century is an age of information
explosion, information technology and network economy
is its enormous power to promote the social economic
form the profound transformation, the electronic
commerce has become the core of information world and
the driving force for the development of network
economy. E-business and the rapid development of
information technology shortens the distance between
enterprises and suppliers, to promote enterprise and
suppliers of information integration and sharing, changing
the enterprise find supplier information and supplier
transaction way, affect the transaction cost, safety and
reliability. Therefore, establishing the new evaluation
standard is to guarantee the successful cooperation,
stability of the important premise.
In the traditional research of supplier selection,
typical fuzzy clustering algorithm are the method based
on similarity relation and fuzzy relation, the maximum
tree method based on fuzzy cam and dynamic
programming etc[1-2]. But the traditional algorithm is not
considered in the evaluation of various factors of the
difference between the, considered in the clustering
process of each factor are equivalent [3]. At the same time,
because of the number of suppliers which involved in
electronic commerce environment is increasing, through
the algorithm step select the best suppliers, will lead to
excessive amount of calculation. Therefore, on the basis
of considering the above two problems, in this paper,
first，the weighted of each index is curtained by AHP, and
then the weight is added to the fuzzy clustering algorithm.
The F-distribution of probability statistics is used to
determine the best classification number, which can help
choose the best classification. Finally, comprehensive
value is computer by fuzzy synthetically evaluation,
through which the best supplier can be selected.
II Establishment of evaluation index system
In the era of network economy and the rapid
development of e-business environment, the evaluation of
supplier information ability should be given enough
attention [4-6]. this paper is based on referencing the
representative index of traditional supplier selection,
specifically from the bright time character, scientific and
practical, flexible operation, expansibility, comprehensive
system five aspects to carry on comprehensive
consideration, try to establish a platform for electronic
commerce supplier evaluation and selection index system
as shown in table I[7]:
TABLE I Index system
Target layer
Rule layer
Informationiz
ation B1
Service level
B2
Supplier A
Index layer
Information construction
investment ratio C1
Computer professionals proportion
C2
Information sharing integrated
ability C3
Information security C4
Industry experience C5
After-sales service satisfaction C6
Historical transaction records C7
Brand reputation C8
Recycling center processing speed
C9
Rapid response ability C10
Business
ability B3
Technology
level B4
Enterprise
development
prospect B5
Cost control C11
Financial status C12
Supply capacity C13
Technology innovation ability C14
Production equipment safe
operation rate C15
R&D Investment ratio C16
Equipment leading level C17
Market influence C18
New product development rate C19
Training expenditure per capita C20
Economic and technological
environment C21
III Identify weight by AHP
This paper uses the geometric average method to
solve the largest eigenvalue λ and the corresponding
characteristic vector W of comparison matrix.
WA=[a1 a2 a3 a4 a5]
WBi=[bi1 bi2 … bin]
IV Establishment of weighted fuzzy clustering model
A Data weighted standardization
Set domain U=（x1,x2,…,xn ） to be classified n
suppliers, each object has a 5level of evaluation index,
according to the problem of the original data matrix:
 x11 x12  x1m 
x
x
 x2 m 
m=5
D   21 22


 


 xn1 xn 2  xnm 
In practical problems, different data generally have
different dimensions. In order to make a different amount
of data can be compared, usually need to make
appropriate transform data. Therefore, according to the
fuzzy matrix requirements for data standardization data
compression to the interval [0, 1], the process requires the
following transformation [8]:
1）Translation · standard deviation changes:
 x  xk
xik  ik
sk
i =1, 2 ,3,…,n; k=1,2,3,4,5
Among them, x k 
1 m
1 n
xik , sk 

 ( xik  x k )2
n i 1
n i 1
After transformation, each variable of the mean
value is 0, the standard deviation is 1, and eliminate the
influence of dimensional, but the X is not necessarily in
the interval [0,1].
2）Translation · differential changes:
xik  min xik 

xik 
1i  n
max xik  min xik 
1i  n
1i  n
0  xik  1
k=1,2,3,4,5
is clearly, and also eliminate the
j=1,2,3,…,n；
And get a fuzzy relations similar matrix R  rij
 
(1)
nn
C Dynamic clustering process [10]
Fuzzy clustering analysis requires the establishment
of fuzzy matrix is reflexive, symmetric and transitive, but
according to (1) type of fuzzy matrix, is a fuzzy similarity
matrix R, not necessarily is transitive, that R is not
necessarily a fuzzy equivalence matrix. In order to
classification, R also needs to be transformed into fuzzy
equivalent matrix R*. Therefore, need to use two leveling
method ( such as type (2) ) on the fuzzy similar matrix R
transformation, and the transitive closure of the t R (R), t
(R) that is seeking a fuzzy equivalence matrix R*,that is
t(R)=R*.
(2)
R  R 2  R 4    R 2( k 1)  R 2k  t R   rij mm
By (2) type get the fuzzy equivalent matrix t(R), t(R)
in numerical arranged from big to small, λ is valued to the
arrangement sequence, can form the dynamic clustering
figure.
D Determine the optimal class number
In determining the classification number, often in
dynamic clustering view, adjust the λ value in order to get
the proper classification, without prior to accurately
estimate the good samples should be divided into several
categories. This method is often in the subjective desire to
classification, and then to make λ, which leads to different
people to the classification, will have the different results.
Thus the proposed F-distribution to determine the optimal
threshold value of λ, then according to the λ value in the
view of dynamic cluster classification, finally get the
optimal class number. The algorithm is as follows [11-13]:
Calculation of the original data matrix to overall
sample center vector, in which:
influence of the dimension. Then, on the transform results
1 n

（k=1,2,3,4,5）
(3)
x

xik 

were weighted arithmetic, get:
 n i 1 
 x11 x12  x1m  a1 0  0   x11 x12  x1m 
Corresponding to the classification of λ set for r,
 x x  x   0 a  0   x x  x 
sample
number of class j is nj, sample set of class j
21
22
2
m
2
21
22
2
m



Y 
 
   
  
  is x1 j  , x2 j  , xn j  ，cluster center vector of class j is

 
 

 j
 j  j
 j
   0 0 0 a m   xn1 xn2  xnm
 
 xn1 xn2  xnm
x  x1 , x 2 ,, x n



B Establishing fuzzy relationship matrix
According to the traditional clustering method to
determine the similarity coefficient, establish fuzzy
similar
matrix.
To
determine
the
similarity
rij  R( xi , x j ) methods mainly have the traditional
cluster analysis of the similarity coefficient method,
distance and angle cosine method. In this paper, using the
included angle cosine method, its algorithm such as
type[9]:
m
rij 
 x  x
ik
k 1
m
 x
k 1
ik
2

jk
i=1,2,3,…,n;
m
 x
k 1
2
jk
 j
1
nj
xk 
nj
 x 
j
ik
（k=1,2,3,4,5）
(4)
1
According to (3) and (4) the type of F-distribution,
get (5)
r
F
n
r
j 1
nj
j
x
 j
 x    x
j
j 1 i 1
i
2
 x  n  r 
 j
2
(5)
 r  1
Its molecular represents the distance between two
classes, denominator represents the distance between the
sample within-class. Therefore, the greater the F value
that the distance between the classes and class is larger,
classification is better.
If F  F r  1, n  r ,   0.05 ,according to the
statistical analysis of variance theory that the difference
between the classes is remarkable, illustrating the
classification more reasonable，If the value which satisfies
the inequality F  F r  1, n  r  is more than one, can
further study the size of ( F  F ) , find a satisfactory F
value from larger.
V Multistage fuzzy comprehensive evaluation
1）The establishment of evaluation set.
Set
evaluation V={v1,v2,v3,v4,v5}={good, better, generally,
worse, bad}={5,4,3,2,1}
2）Statistics, determine the single factor evaluation
membership vector[14-15], and formed the membership
degree matrix R
Membership degree in fuzzy comprehensive
evaluation is the most important and basic concept. The
so-called membership rij , refers to a plurality of
evaluation main body to a certain evaluation object in the
factor set to V assessment probability. Membership
7
vector R  r , r ,, r , i  1,2,, n, r  1 ,membership
 ij
i
i1 i 2
im
j 1
matrix R=(R1，R2，…，Rn)T=(rij)
3）One stage fuzzy comprehensive evaluation
According to the original data to determine the
solution of one stage membership fuzzy matrix RBij of
each scheme, get : Bi  WBi Rij
4）Two stage fuzzy comprehensive evaluation
Let one stage results constitute two stage single
factor judgment matrix RA  [B1 B2 B3 B4 B5], A  WA RA
5）Calculation of comprehensive score
E  AV T
According to the comprehensive score height can
determine various schemes, so as to select an optimal
supplier.
VI Summary
Considering the fuzzy clustering algorithm can't
distinguish between the data itself attribute imbalance,
based on this algorithm with weighted fuzzy clustering
and comprehensive evaluation method, the method of
electronic commerce environment to select suppliers, this
method can various factors taken into account, the
objective reaction actual situation, the classification of the
real problem can be more accurate.
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